{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# AllDifferent\n",
    "\n",
    "In this notebook, we take a quick look onto the AllDifferent (`all_different`) constraint on the example of the graph coloring problem.\n",
    "We especially analyze the effect of the automatic `all_different` inference.\n",
    "If you are using `!=` instead of `all_different`, CP-SAT will automatically try to find large cliques of variables that are all different and add them as `all_different` constraints.\n",
    "This is significantly faster than adding non-optimized `all_different` constraints manually.\n",
    "This optimization gets disabled as soon as a single `all_different` constraint is added manually, and we can see that the solver is significantly slower.\n",
    "Thus, only use `all_different` if you do it properly on large sets of variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Graph Coloring Problem\n",
    "\n",
    "The **Graph Coloring Problem** is a classic combinatorial optimization problem in computer science and graph theory. It involves assigning colors to the vertices of an undirected graph in such a way that no two adjacent vertices share the same color while using the fewest number of colors possible.\n",
    "\n",
    "## Problem Statement\n",
    "\n",
    "Given an undirected graph G = (V, E), where V represents the set of vertices and E represents the set of edges, the objective is to find a coloring function C: V -> {1, 2, ..., k} such that:\n",
    "\n",
    "1. For each vertex v ∈ V, C(v) is an integer representing the color assigned to vertex v.\n",
    "2. For all edges (u, v) ∈ E, C(u) ≠ C(v), meaning adjacent vertices must have different colors.\n",
    "\n",
    "## Objective\n",
    "\n",
    "Minimize the number of colors (k) used in the coloring while satisfying the above conditions. This minimum value of k is referred to as the **chromatic number** of the graph, denoted as χ(G).\n",
    "\n",
    "## Applications\n",
    "\n",
    "Graph coloring problems have numerous practical applications in various domains, including:\n",
    "\n",
    "- Scheduling of tasks with resource constraints.\n",
    "- Register allocation in compiler optimization.\n",
    "- Frequency assignment in wireless communication.\n",
    "- Timetabling in educational institutions.\n",
    "- Map coloring in cartography.\n",
    "\n",
    "## Complexity\n",
    "\n",
    "The Graph Coloring Problem is NP-hard, which means that finding the optimal coloring in the fewest colors is computationally challenging. It falls within the broader class of NP-hard problems and is used as a benchmark for testing the efficiency of algorithms and heuristics.\n",
    "\n",
    "Researchers in computer science and operations research continue to develop algorithms and approaches to solve instances of the Graph Coloring Problem efficiently and find approximate solutions for large graphs.\n",
    "\n",
    "For more details and formal algorithms related to the Graph Coloring Problem, please refer to academic literature and research papers in the field of combinatorial optimization and graph theory.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "from ortools.sat.python import cp_model\n",
    "\n",
    "\n",
    "def solve_coloring(\n",
    "    g: nx.Graph,\n",
    "    use_all_different: bool,\n",
    "    disable_infer_diff: bool = False,\n",
    "    add_single_all_different: bool = False,\n",
    ") -> int:\n",
    "    \"\"\"\n",
    "    Solves the graph coloring problem for the given graph.\n",
    "    :param g: the graph to color\n",
    "    :param use_all_different: whether to use the all_different constraint or != constraint\n",
    "    :param disable_infer_diff: whether to disable the all_different constraint inference for !=\n",
    "    :param add_single_all_different: whether to add a single all_different constraint\n",
    "    \"\"\"\n",
    "    model = cp_model.CpModel()\n",
    "    # specify valid coloring\n",
    "    x = [model.new_int_var(0, g.degree[v] - 1, f\"v{v}\") for v in g.nodes()]\n",
    "    for v, w in g.edges():\n",
    "        if use_all_different:\n",
    "            model.add_all_different([x[v], x[w]])\n",
    "        else:\n",
    "            model.add(x[v] != x[w])\n",
    "    if add_single_all_different:\n",
    "        # adding a single all_different will disable the inference of all_different\n",
    "        # for the != constraint and drastically increase the runtime\n",
    "        v, w = next(iter(g.edges()))\n",
    "        model.add_all_different([x[v], x[w]])\n",
    "    # minimize the maximum color\n",
    "    max_x = model.new_int_var(0, max(g.degree[v] for v in g.nodes()), \"xc\")\n",
    "    model.add_max_equality(max_x, x)\n",
    "    model.minimize(max_x)\n",
    "    # set up solver\n",
    "    solver = cp_model.CpSolver()\n",
    "    if disable_infer_diff:\n",
    "        solver.parameters.infer_all_diffs = False\n",
    "    solver.parameters.max_time_in_seconds = 300\n",
    "    # solver.parameters.log_search_progress = True\n",
    "    # solver.log_callback = print\n",
    "    # solver\n",
    "    status = solver.solve(model)\n",
    "    return status"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = nx.connected_caveman_graph(35, 35)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "\n",
    "nx.draw(g, with_labels=False, pos=nx.spring_layout(g), node_size=5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 36min 56s, sys: 25.2 s, total: 37min 21s\n",
      "Wall time: 5min\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solve with all_different on every edge\n",
    "%time solve_coloring(g, use_all_different=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.91 s, sys: 114 ms, total: 4.02 s\n",
      "Wall time: 1.23 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solve with != on every edge (all_different inference)\n",
    "%time solve_coloring(g, use_all_different=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 37min 4s, sys: 24.3 s, total: 37min 29s\n",
      "Wall time: 5min\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solve with != on every edge (all_different inference disabled)\n",
    "%time solve_coloring(g, use_all_different=False, disable_infer_diff=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 36min 52s, sys: 25.3 s, total: 37min 18s\n",
      "Wall time: 5min\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solver with != on every edge plus a single all_different (all_different inference is not explicitly disabled, but will be disabled because of the single all_different)\n",
    "%time solve_coloring(g, use_all_different=False, add_single_all_different=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "mo",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
